Question

The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 44 bears has a mean weight of 188.5 lb. At α = .03, can it be concluded that the average weight of a bear in Yellowstone National Park is different from 187 lb? Note that the standard deviation of the weight of a bear is known to be 8.5 lb.

(a) Find the value of the test statistic for the above hypothesis.

(b) Find the critical value.

(c) Find the p-value.

(d) What is the correct way to draw a conclusion regarding the above hypothesis test? Problem #3(a): test statistic (correct to 2 decimals) Problem #3(b): critical value (correct to 2 decimals) Problem #3

(c): p-value (correct to 4 decimals) (A) If the answer in (c) is less than 0.03 then we cannot conclude at the 3% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (B) If the answer in (c) is greater than 0.03 then we conclude at the 3% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (C) If the answer in (a) is greater than the answer in (c) then we cannot conclude at the 3% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (D) If the answer in (b) is greater than the answer in (c) then we cannot conclude at the 3% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (E) If the answer in (a) is greater than the answer in (b) then we cannot conclude at the 3% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (F) If the answer in (a) is greater than the answer in (b) then we conclude at the 3% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (G) If the answer in (a) is greater than the answer in (c) then we conclude at the 3% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb. (H) If the answer in (b) is greater than the answer in (c) then we conclude at the 3% significance level that the average weight of a bear in Yellowstone National Park is different from 187 lb.

Answer 1

Ho:mu=187

Ha:mu not =187

alpha=0.03

(a) Find the value of the test statistic for the above hypothesis.

z=xbar-mu/sigma/sqrt(n)

z=(188.5 -187 )/(8.5 /sqrt(44))

z=1.17

(b) Find the critical value.

=NORM.S.INV(0.015)

=-2.170

Z crit for two tail

|Z|>2.170

(c) Find the p-value.

2*(1-righttail prob)

=2*(1-=NORM.S.DIST(1.17,TRUE))

=2*(1-0.87912)

=0.2418

p=0.2418

here test statistc<z critical

Do not reject Ho

p>alpha

Do not reject Ho

No suufcient evidence to support the claim at 5% level of significance